Estimating ﬂood damage to railway infrastructure – the ...

Nat. Hazards Earth Syst. Sci., 15, 2485–2496, 2015

www.nat-hazards-earth-syst-sci.net/15/2485/2015/

doi:10.5194/nhess-15-2485-2015

© Author(s) 2015. CC Attribution 3.0 License.

Estimating flood damage to railway infrastructure – the case study

of the March River flood in 2006 at the Austrian Northern Railway

P. Kellermann1, A. Schöbel2, G. Kundela3, and A. H. Thieken1

1Institute of Earth and Environmental Science, University of Potsdam, Karl-Liebknecht-Straße 24–25,

14476 Potsdam-Golm, Germany2Open Track Railway Technology GmbH, Kaasgrabengasse 19/8, 1190 Vienna, Austria3ÖBB-Infrastruktur AG, Praterstern 3, 1020 Vienna, Austria

Correspondence to: P. Kellermann ([email protected])

Received: 30 March 2015 – Published in Nat. Hazards Earth Syst. Sci. Discuss.: 16 April 2015

Accepted: 29 October 2015 – Published: 10 November 2015

Abstract. Models for estimating flood losses to infrastruc-

ture are rare and their reliability is seldom investigated al-

though infrastructure losses might contribute considerably

to the overall flood losses. In this paper, an empirical mod-

elling approach for estimating direct structural flood dam-

age to railway infrastructure and associated financial losses

is presented. Via a combination of event data, i.e. photo-

documented damage on the Northern Railway in Lower Aus-

tria caused by the March River flood in 2006, and simu-

lated flood characteristics, i.e. water levels, flow velocities

and combinations thereof, the correlations between physical

flood impact parameters and damage occurred to the rail-

way track were investigated and subsequently rendered into

a damage model. After calibrating the loss estimation using

recorded repair costs of the Austrian Federal Railways, the

model was applied to three synthetic scenarios with return

periods of 30, 100 and 300 years of March River flooding.

Finally, the model results are compared to depth-damage-

curve-based approaches for the infrastructure sector obtained

from the Rhine Atlas damage model and the Damage Scan-

ner model. The results of this case study indicate a good per-

formance of our two-stage model approach. However, due

to a lack of independent event and damage data, the model

could not yet be validated. Future research in natural risk

should focus on the development of event and damage doc-

umentation procedures to overcome this significant hurdle in

flood damage modelling.

1 Introduction

Railway infrastructure plays a crucial role in ensuring trans-

portation of people and goods and, thus, contributes to eco-

nomic and societal welfare. River floods, however, pose a

great threat to the network’s reliability and continuously

cause significant direct damage (Nester et al., 2008; Moran

et al., 2010a, b). In 2006, for example, a 100-year flood

event occurred at the lower reach of the river March, which

is located at the border of (Lower) Austria and Slovakia.

During this event, the average flow rate of 108 m3 s−1 of

the March in this section was exceeded nearly 13 times re-

sulting in a peak flow rate of 1400 m3 s−1. The maximum

water level lasted for nearly 2.5 days and flow velocities

were rather low (Godina et al., 2007). The flood affected

an important connection line of the Austrian Federal Rail-

ways (ÖBB) between Vienna and the Czech Republic, the

Northern Railway, along a section of around 10 km caus-

ing repair costs of more than EUR 41.4 million (Moran et

al., 2010a; ÖBB-Infrastruktur AG, personal communication,

2014) and a complete shutdown of passenger and freight op-

erations for several months (Moran et al., 2010b). This event

fully demonstrates the high vulnerability of railway infras-

tructure to floods. Hence, there is a clear need for valuable

information on potential risk hot spots as well as on expected

flood damage in order to support strategic decision-making

in flood risk management.

Modelling flood damage to transportation infrastructure,

however, is mostly neglected in natural hazards and risks re-

search so far. Merz et al. (2010) indicated that knowledge

Published by Copernicus Publications on behalf of the European Geosciences Union.

2486 P. Kellermann et al.: Estimating flood damage to railway infrastructure – Austrian Northern Railway

of damage mechanisms as well as crucial in-depth informa-

tion and data for the development of appropriate model ap-

proaches is still scarce in the infrastructure sector, where-

upon existing approaches are still subject to very high un-

certainties. Kunert (2010) outlined that mainly unit loss as-

sessments can be found in literature, whereas (empirical)

flood damage functions have widely been used for loss es-

timation in the residential sector. A popular example is the

Multi-Coloured Manual (MCM), the most advanced method

for flood damage estimation within Europe (e.g. Penning-

Rowsell and Chatterton, 1977; Penning-Rowsell et al., 1992,

2005, 2010, 2013; Jongman et al., 2012). Therein, direct

flood damages in the transport infrastructure sector are only

roughly estimated by a percentage share of property losses on

the basis of empirical data of the summer floods in the UK in

2007 (Jongman et al., 2012). However, the focus of the MCM

lies on the estimation of indirect losses due to traffic disrup-

tions (e.g. additional travel time). A few established flood

damage models, e.g. the Rhine Atlas damage model (RAM)

or the Damage Scanner model (DSM), actually do also con-

sider direct damage to infrastructure by use of depth-damage

curves. However, only aggregated CORINE land-use data

containing a large variety of urban infrastructure and lifeline

elements are used therein (Bubeck et al., 2011; Jongman et

al., 2012). Due to the missing distinction of sub-classes in the

CORINE Land Cover data, there is no detailed information

on the share of damage to transport infrastructure in these

model outputs. By reviewing the recorded losses of the Elbe

flood of 2002 and the contributions of damage categories

to overall losses, Bubeck et al. (2011) showed that both the

RAM and the DSM significantly underestimate the share of

damage corresponding to infrastructure, since the models re-

sult in a share of 1.6 % (RAM) and 2.1 % (DSM). How-

ever, the share of damage to infrastructure alone amounted

to around 14 % (national) and 17 % (municipal) during the

2002 floods (Pfurtscheller and Thieken, 2013). With respect

to the Elbe flood in 2002, the damage to municipal infrastruc-

ture even comprised about 20 % of overall losses (Bubeck et

al., 2011). Since roads and bridges incurred the greatest share

in the infrastructure sector during the Elbe flood, Bubeck et

al. (2011) concluded that using land-use maps as input data

consisting of aggregated information on asset values as well

as coarse resolution only insufficiently reflects damage to lin-

ear structures.

The case study presented in this paper aims to develop

a tool for the estimation of direct flood damage and losses

to railway infrastructure derived from empirical flood dam-

age data – the so-called RAIL model (RAilway Infrastruc-

ture Loss). Using a photographic documentation of structural

damage to the double-tracked Northern Railway line caused

by the March River flooding of 2006, the damage informa-

tion was classified into three different damage grades. Subse-

quently, the correlations of the (simulated) hydraulic impacts

of the event and the damage grades were investigated. After

identification of the most meaningful impact parameters, we

performed a set of kernel density estimations to determine

the decisive thresholds of impact parameter values leading

to a specific structural damage class. Finally, the structural

damage classes were linked to direct economic losses and,

together with the parameter thresholds, rendered into a dam-

age model. The resulting model RAIL is capable of estimat-

ing

– expected structural damage for the standard cross-

section of railway track sections and

– resulting repair costs.

This two-stage approach allows a consideration of both struc-

tural damage types and direct economic losses. Particularly

the first step provides new information on the occurrence

of specific flood damage grades at exposed track sections.

These can then be used for different risk management pur-

poses, e.g. for the planning of (targeted) technical protection

measures. The model development with the underlying data

and statistics is described in detail in the following chapter.

Then, the RAIL model is applied to reanalyse the losses due

to the March flooding in 2006 as well as to estimate direct

flood damage to the Northern Railway and respective finan-

cial losses in cases of a 30-, 100- and 300-year flood event.

Finally, the model performance is compared with the depth-

damage-curve-based approaches of both the RAM and the

DSM and initial conclusions for flood loss estimation in the

railway transportation sector are drawn.

2 Model development

2.1 Classification of structural damage

Comprehensive research in modelling flood damage in the

residential sector shows the methodological expedience to

distinguish between different object classes (e.g. building

types) in the model framework (e.g. Kelman and Spence,

2004; Merz et al., 2004; Maiwald and Schwarz, 2008). Ac-

cordingly, considering the general importance of certain sys-

tem components for rail operations, Moran et al. (2010a) dif-

ferentiate between five main classes of rail infrastructure ele-

ments: standard cross-sections, bridges, station buildings, in-

terlocking blocks and transformer substations. For each of

these components, different states of structural flood damage

were determined in discussions with railway operators and

engineers (see Moran et al., 2010a, b). For example, a revised

version of the structural damage at standard cross-sections,

which will be the focus of this paper, is depicted in Fig. 1.

A railway track’s standard cross-section consists of the ele-

ments substructure, superstructure, catenary and signals. The

left box in Fig. 1 illustrates the damage class 1, where the

track’s substructure is (partly) impounded, but there is no or

only little notable damage. In the middle box, the damage

class 2 is depicted. The substructure and superstructure of

the track section are fully inundated and significant structural

Nat. Hazards Earth Syst. Sci., 15, 2485–2496, 2015 www.nat-hazards-earth-syst-sci.net/15/2485/2015/

P. Kellermann et al.: Estimating flood damage to railway infrastructure – Austrian Northern Railway 2487

Figure 1. Damage classification scheme (adapted from Moran et al., 2010a).

damage at least to the substructure must be expected. Finally,

the right box sketches the damage class 3. Additional dam-

age to the superstructure, catenary and/or signals must be ex-

pected here and, most commonly, the standard cross-section

of the affected track section needs to be completely restored.

The classes are designed for the purpose of fast and practical

in-field damage assessments and scaled ordinally by progres-

sion of damage.

Using the March River flood at the Northern railway

in 2006 (see introduction) as an example, the occurrence

of these three damage classes was mapped based on a

photographic documentation of the Austrian Federal Rail-

ways (ÖBB). These nearly 100 resulting photographs were

used to evaluate and classify the structural damage at af-

fected track sections. First, the damage patterns depicted in

the photographs were georeferenced in the geoinformation

system (GIS) ArcGIS 10.1 by means of distance markers

along the Northern Railway track. Next, these damage data

were assigned to point features, whereby each point repre-

sents a track segment with a length of 100 m and the high-

est damage pattern within each segment was decisive for the

classification. In a final step, the generated damage points

were each assigned to the damage class matching best, in ac-

cordance with the damage classification scheme (see Fig. 1).

2.2 Hydraulic impact data

The investigation of cause and effect relations between flood-

ing and damage to railway standard cross-sections requires

detailed information on the magnitudes of flood impact

parameters at relevant damage spots. Similar to Kreibich

et al. (2009), we investigated the relation between struc-

tural damage and five potential hydraulic impact parameters,

i.e. water level, flow velocity, energy head, intensity and indi-

cator of flow force, whereby the three latter ones are different

combinations of water level and flow velocity using the fol-

lowing formulae:

energy head : E = h+ v2/2g, (1)

intensity : I = v ·h, (2)

indicator for flow force : IF= h · v2, (3)

where h is water level [m], v is flow velocity [m s−1] and g is

acceleration of gravity= 9.81 m s−2.

Since the above-mentioned event and damage documen-

tation from the ÖBB provide no quantitative information on

such flood characteristics, a transient hydraulic simulation of

the March flood in 2006 was consulted. The simulation was

calibrated on the basis of the March flood waves in 1997 and

1999. During the flood in 2006, three breaches occurred at

different times along the flood protection levee at the March

River (see Fig. 5), which partly influenced the waveform of

the event and, thus, were also considered in the simulation.

However, since only scarce information on the exact size of

the breaches and their development over time was available,

they could only be reproduced with limited accuracy (Humer

and Schwingshandl, 2009a). The model validation was car-

ried out by using recorded discharge data at the gauges Ho-

henau, Angern, Baumgarten, Marchegg and Dürnkrut as well

as observed peak water levels along the river channel dur-

ing the flooding in 2006. The temporal evolvement of the

flood wave was reproduced very well (Humer and Schwing-

shandl, 2009a). The peak water levels were overestimated by

the model by around 8 to 12 cm, depending on the reference

gauge (Humer and Schwingshandl, 2009a).

Using the simulated water levels and flow velocities for

the entire flood area on a 1 m grid as input data, the combined

parameters (i.e. E, I and IF) were computed in ArcGIS 10.1

Raster Calculator.

2.3 Derivation of the damage model

The development of the flood damage model is essentially

based on the significance of the correlation between the hy-

draulic flood impact and empirical damage patterns that oc-

curred in 2006. Within the GIS, the Northern Railway is rep-

resented as a common linear feature. In order to account for

the width of a multi-track standard cross-section and its po-

tential impact area for floods, a spatial extension, i.e. a buffer

zone, needs to be attached to each segment’s side facing the

www.nat-hazards-earth-syst-sci.net/15/2485/2015/ Nat. Hazards Earth Syst. Sci., 15, 2485–2496, 2015


March River. Since this spatial limitation of causality is the

decisive factor for the model’s validity, the buffer width has

to be chosen sensibly. We therefore extracted hydraulic in-

put data by using buffer widths of 5, 10, 20, 50 and 100 m in

order to test the sensitivity of this factor to the significance

of the correlations. By overlapping the buffer polygons with

the hydraulic raster data of the March flood of 2006, those

without at least a partial exposure to the simulated inundated

area were excluded and the remaining polygons were taken

as the relevant impact areas in the hydraulic simulation. Next,

basic descriptive statistics were calculated for the extracted

parameter values, whereby the respective mean values of all

pixels of the five chosen flood impact parameters that (at least

partly) overlap a buffer zone were further considered in the

model development. In addition, the maximum values were

also checked and differences will be briefly discussed.

The idea of the proposed flood damage model RAIL is

to identify statistically significant correlations between dif-

ferent flood impacts and structural damage classes using the

data basis described in the Sects. 2.1 and 2.2. Since the de-

pendent variable (structural damage) is given on an ordinal

scale, the nonparametric Spearman’s rank correlation coeffi-

cient (also: Spearman’s rho) was used to perform this anal-

ysis, whereby a correlation with a coefficient equal or supe-

rior to 0.5 was considered to be meaningful. Based on these

criteria, the major purpose of our approach was to initially

estimate the structural damage class to be expected for a

given impact at exposed track sections. Since the damage

classification (see Sect. 2.1 and Fig. 1) is discrete and dis-

tinct, the use of steady curve progressions (e.g. regression

models) is not suitable to describe the damage evolution. In-

stead, we strive to derive clear thresholds of parameter val-

ues for the assignment of an unambiguous damage class to

each track segment granting sufficient validity of the model

framework. Hence, we performed a set of kernel density esti-

mations (KDE) to compute the empirical probability density

distributions (Gaussian kernel) for the values of the impact

parameters for each of the three damage classes. The inter-

sections of the individual curves were subsequently used to

determine the thresholds of parameter values in the RAIL

model to assign the most likely structural damage class to

each track segment.

In the final step of the model development, a financial

loss was estimated for each structural damage class. Hereby,

the following standard costs were considered: (1) costs of

loss assessment/documentation, (2) cost for track cleaning

per running metre (rm) and (3) standard cross-section repair

costs per rm as defined by Austrian railway infrastructure ex-

perts (BMLFUW, 2008). These three cost types were individ-

ually combined for each damage class according to the cor-

responding damage pattern (see Fig. 1). Table 1 shows both

the combined standard costs of a double-tracked segment per

rm and the resultant costs for a 100 m track segment for all

three damage classes.

Table 1. Standard repair costs per 100 m segment of a double-

tracked railway standard cross-section. The costs of damage class 1

are attributable to damage documentation and cleaning of the track

segment. The standard repair costs for damage class 2 were already

calibrated by adding a coefficient of 0.25 (see Sect. 2.4). The cost

value for damage class 3 complies with the overall damage potential

of a 100 m track segment, including costs for damage documenta-

tion and cleaning.

Damage class 1 Damage class 2 Damage class 3

Costs per

100 m EUR 11 700 EUR 135 550 EUR 702 200

segment

2.4 Calibration of loss estimates

Since the substructure is the most expensive system compo-

nent of a railway standard cross-section, it requires special

attention regarding its notably high weighting within the es-

timation of repair costs. In other words, the individual dam-

age grade of the affected substructure can significantly bias

the loss estimation, particularly because the underlying ta-

ble of standard costs for the calculation only contains costs

of full restoration providing no further graduation of costs

for minor repairs (e.g. tamping of the substructure). How-

ever, when a track segment is classified as damage class 2,

implying a substantial damage to the substructure, it is not

fully assured that full restoration is definitely required. Our

approach was, therefore, to calibrate the loss estimates by

determining a proportional factor for damage to the substruc-

ture in damage class 2 on the basis of empirical loss data of

the March River flood in 2006. By knowing the exact length

of the damaged track section, the individual damage grade

of the track segments as well as the total repair costs of the

ÖBB, the model’s boundary conditions could be set com-

mensurate with the event. This was necessary as not all seg-

ments, which are exposed to flooding, were damaged during

the March flood mainly due to effective flood protection mea-

sures. Now being applied with varying coefficients of cost

calculation for the restoration of the substructure (damage

class 2), the model was iteratively adjusted to the real ex-

penses.

2.5 Comparing the RAIL model to RAM and DSM

Information on damage to the infrastructure sector has only

been scarcely considered in flood damage modelling so far

(see Sect. 1). However, initial approaches are being imple-

mented, for example, in the RAM and the DSM. The pre-

sented damage model RAIL was compared to these two mod-

els from ICPR (2001) and Klijn et al. (2007) in order to ob-

tain comparative values and a further performance indication.

The RAM was developed for the International Commis-

sion for the Protection of the Rhine (ICPR, 2001; Bubeck et



Figure 2. Damage curves used in the Rhine Atlas (left panel) and the Damage Scanner model (right panel) (adopted from Bubeck et al.,

2011).

al., 2011). Derived from the empirical flood damage database

HOWAS, the depth-damage functions were created to es-

timate direct tangible flood damage potentials for five re-

classified CORINE land-use classes depending on inunda-

tion depths (ICPR, 2001; Bubeck et al., 2011). Each of the

functions is linked to a certain value of maximum damage

(damage potential) in order to calculate the absolute loss per

grid cell. The damage potential in the RAM was derived

from gross underlying asset values as at 2001 (ICPR, 2001).

Additional information on the RAM can be found e.g. in

ICPR (2001) or Bubeck and de Moel (2010). Figure 2 (left

panel) shows the damage curve in RAM for the land-use type

“traffic”, which corresponds to the infrastructure sector.

The DSM is based on the standard software for estimation

of flood damage in the Netherlands, the Highwater Informa-

tion System – Damage and Casualties Module (HIS-SSM)

(Jongman et al., 2012). It was developed to obviate the dis-

advantage of the HIS-SSM model to require highly detailed

input data on individual asset units. Due to limited availabil-

ity of data on the object scale, the DSM uses only aggregated

land-use data as inputs and is designed for estimations at the

regional scale (Jongman et al., 2012). Differently from the

RAM, this damage model has a more synthetic origin of de-

velopment as its depth-damage functions are mainly derived

from expert judgement, although some empirical information

was used, too (Bubeck et al., 2011). Figure 2 (right panel)

illustrates the damage curve shape for the land-use class “in-

frastructure”. Further information on the DSM is provided

e.g. in Klijn et al. (2007) or Bubeck and de Moel (2010).

Both the RAM and the DSM estimate monetary losses by

calculating the ratio of a predefined maximum damage de-

pending on the particular inundation depths. In order to fa-

cilitate the comparison of RAM and DSM with the RAIL

model, the two individual damage potentials for infrastruc-

ture were replaced by the ÖBB standard cross-section repair

costs (see Table 1). Following the rationale that the damage

potential of a railway track is a constant value, the model

comparison is now based on the same price level. In a next

step, the water levels from the hydraulic simulations were

used as input for the infrastructure damage functions to cal-

culate both total costs and respective difference factors to the

RAIL model.

3 Statistical review and model adjustments

In this section, the results of the statistical review of the

model setup and consequential model adjustments are pre-

sented.

The classification of structural damage on the basis of

the photographic documentation (see Sect. 2.1) resulted in

a sample size of 37 damage segments. After both the (depen-

dent) variable damage class and the (independent) variables

of flood impact were tested positive on normal distribution

(Shapiro–Wilk test), the correlation coefficients were deter-

mined on the basis of Spearman’s rho. Table 2a provides all

Spearman’s rho values resulting from the sensitivity analysis

on buffer widths. The analysis revealed that both the strength

and the direction of the correlation react very sensitively to

the size of the area considered for potential flood impact. On

the whole, it is notable that the correlation coefficients are

strongly decreasing with increasing buffer width. However,

there is a temporary increase in Spearman’s rho for the buffer

width of 20 m for the parameters v, I and IF. From a width of

50 m the coefficients even begin to turn negative, which runs

counter to the physical rationale of damage development.

Solely the coefficients concerning the parameters h and E

meet the defined threshold for at least some buffer widths,

whereas the parameters v, I and IF are considerably below

the threshold level of significance throughout all widths. The

5 m buffer obtained slightly higher coefficients than the 10 m

variant. However, since the inner boundary of the buffers are

set to the centre of the track lane, the buffer width of 5 m

would be insufficient to cover the entire rail embankment

and, thus, to enclose all elements of the cross-section ade-

quately. Due to this technical consideration, the buffer width

of 5 m was neglected in retrospect as considered to be too



Figure 3. Box plots displaying the summary statistics of each impact parameter per damage class and for varying buffer widths.

narrow to represent the double-track standard cross-section

of the Northern Railway adequately.

The summary statistics of the mean parameter values per

damage class are illustrated by the box plots in Fig. 3.

Therein, only the median of h and E increases with increas-

ing damage classes and, thus, is corresponding to the general

logic of damage evolution. All other parameters are contra-

dictory to it since the median values partly decrease with in-

creasing damage. Furthermore, the box plots clearly indicate

a varying scatter range of the data as well as different natures

of distribution for different buffer widths of the same param-

eter since both the lengths of the box plots and the position

of the medians within the interquartile range diversify signif-

icantly. Considering these criteria, the 10 m buffer width fea-

tures lower data scattering and lesser distributional skewness

than widths of 20 m and higher. In damage classes 1 and 2

the samples of 5, 10 and 20 m width are nearly normally dis-

tributed, whereas the widths of 50 and 100 m already show a

distributional skewness in the data. In damage class 3, how-

ever, all box plots indicate a skewed distribution of parame-

ter values to a greater or lesser extent. Based on the shown

characteristics, the buffer width of 10 m was selected for in-

vestigation of the parameters h and E, and the parameters v,

I and IF are excluded from the further investigations.

As already described in Sect. 2, the identification of rel-

evant flood impacts is based on transient hydraulic data,

whereby the mean parameter values within the buffers were

used for the model development. This method was chosen

with the objective to reduce possible effects of very small-

scale extremes in the high-resolution input data caused, for

example, by cavities. However, maximum impacts might be

more relevant for the extent of damage than mean values. Yet,

in order to legitimise the use of mean values, the maximum

values were also investigated. Table 2b provides the resulting

correlation coefficients. In relative terms, the situation is sim-

ilar to the findings on the basis of mean impacts, since h and

E still show the highest correlation coefficients of all param-

eters and small buffer widths lead to better results than large

buffer widths. In absolute terms, however, none of the combi-

nations are meeting the defined threshold of significance of

correlation and, thus, the maximum parameter values were

not considered in the further course of this work.



Figure 4. Kernel density plots for the impact parameters h and E. The parameter values at the marked graph intersection points determine

the thresholds in the damage model to assign the most likely damage class to each track section. The derived values apply equally to both

parameters.

After identifying the impacts of concern and verifying the

reference area, a KDE was performed for each parameter and

damage class to derive probability-based thresholds of pa-

rameter values for the damage model. The resulting proba-

bility density plots are shown in Fig. 4. The black marks in

the plot highlight the curve intersections being decisive for

the threshold determination. It is apparent that there is al-

most no disparity perceptible between the curve shapes of

the probability densities. As E has an additive interrelation

to v – being very low for the March River flood in 2006 –

its values only differ marginally from the inundation depths,

which explains the close similarities of the graphs. Assessing

the curve progressions also points to some characteristics in

the data basis. First, differing shapes of the probability den-

sity curves are apparent showing a narrow shape for damage

class 1 along with a broader span for the damage classes 2

and 3. Secondly, the curve amplitudes vary greatly between

damage class 1 and damage classes 2 and 3. This can be ex-

plained by (1) the very uneven sample sizes of the individual

damage classes resulting from the classification of the pho-

tographically documented damage information according to

the formulated scheme (see Fig. 1) and (2) the overall co-

efficient of variation (0.66) of the hydraulic data within the

reference areas, which is relatively high.

Overall, a few questions still remain unanswered and some

key assumptions concerning the model basis could not be

validated so far. First, it was taken as granted that the corre-

lations being investigated imply causality, although the pos-

sibility remains that unidentified parameters, certain precon-

ditions of the test track structure or other unknowns could

have been either the main cause of the damage occurrence

or, at least, of partial influence. Indications thereof include

the rather low correlation coefficients as the chosen impact

parameters just reach the defined threshold of significance

as well as the fact that data scattering is noticeably increas-

ing and distributional skewness is arising in damage class 3.

Second, there are other considerable impact parameters, such

as significant flow velocities or duration of the flood impact.

However, during the March River flood in 2006 only very low

flow velocities occurred within the track’s impact area with

the result that no meaningful correlations could be found

(see Table 2a). This parameter was therefore discarded in the

model development. Both examples would presumably have

at least some influence on damage patterns. Third, the data

basis for loss estimation may contain considerable uncertain-

ties. While the calculation of monetary losses is based on a

table of standard costs for damage to individual infrastructure

elements (see Sect. 2.3 and Table 1), its calibration was con-

ducted using a single amount of total loss without detailed

information on e.g. the composition of this amount, possible

discounts or other price concessions. Finally, another source

of uncertainty can be the missing information on the vertical

extent of the track in GIS. The particular height of the track

in relation to the surrounding area might change over course

due to e.g. the substructure being section-wise located below

surface or, reciprocally, on existing railroad embankments. In

such a case, the identified local water levels are significantly

biased as their reference height is the ground level.

4 Application and evaluation

4.1 The March flood of 2006

The developed flood damage model RAIL was initially run

with the hydraulic input of the March River flood of 2006 in

order to evaluate its performance in loss estimation. For this,



Table 2. Spearman’s rank correlation coefficients between the de-

pendent variable “damage class” and each independent variable

“impact parameter” based on the mean values (a) and maximum

values (b) for varying buffer widths. The coefficients meeting the

threshold level of meaningfulness, which has been set to 0.5 within

this study, are highlighted in bold type. Additionally, the corre-

sponding p values (two-tailed, 5 % error) are provided in brackets

and in italics.

Buffer 5 m 10 m 20 m 50 m 100 m

width

(a) Damage class (n= 37)

h0.532 0.5 0.381 0.096 −0.066

(0.001) (0.002) (0.020) (0.572) (0.696)

v0.104 0.095 0.169 −0.106 −0.159

(0.539) (0.578) (0.318) (0.531) (0.347)

I0.334 0.323 0.399 −0.098 −0.172

(0.043) (0.051) (0.014) (0.562) (0.308)

IF0.261 0.090 0.216 −0.152 −0.239

(0.119) (0.597) (0.199) (0.371) (0.154)

E0.532 0.505 0.381 0.091 −0.066

(0.001) (0.002) (0.020) (0.590) (0.696)

(b) Damage class (n= 37)

h0.398 0.319 0.079 −0.238 −0.136

(0.015) (0.055) (0.641) (0.157) (0.423)

v0.188 0.110 0.064 −0.332 −0.315

(0.266) (0.517) (0.705) (0.045) (0.058)

I0.300 0.170 −0.020 −0.302 −0.299

(0.071) (0.314) (0.909) (0.069) (0.072)

IF0.251 0.147 −0.111 −0.300 −0.308

(0.134) (0.385) (0.511) (0.071) (0.063)

E0.393 0.313 0.079 −0.232 −0.136

(0.016) (0.059) (0.641) (0.166) (0.423)

we compared the estimated total loss with recorded repair

costs of the ÖBB incurred by this event. The results showed

that the model overestimates the real loss by a factor of ap-

proximately 1.6, which indicated the need for further adjust-

ments. Therefore, we calibrated the model by means of iter-

atively fitting its loss estimation in damage class 2 to the real

expenses (see Sect. 2.4). The calibration resulted in a cost re-

duction of 75 % in this damage class. The overestimation bias

of the RAIL model could thereby be reduced from the initial

60 % to approximately 2 %. The result of the (calibrated) loss

estimation is provided in Table 3a. Additionally, the model

results for the March flood data are cartographically mapped

in Fig. 5 showing the inundation areas including water levels

as well as classified damage at flood-affected track segments.

Figure 5. Estimation of damage potentials at the Northern Rail-

way for the hydraulic conditions of the March River flood in 2006.

During the event, three levee breaches occurred at three different

locations along flood protection levee at the March River (see pink

dots).

Although this event is classified as a 100-year event ac-

cording to the observed discharge at the gauge Angern, the

inundation area in the northern half of the river section con-

siderably differs compared to the synthetic 100-year event

(see Fig. 6 and Sect. 4.2). While the respective area was

not flooded in 2006, the synthetic scenario discloses wide-

scale inundation in this section. This is due to the difference

in the underlying assumptions of levee breaches in the sim-

ulations. The hydraulic remodelling of the real flooding in

2006 considers the three actual levee breaches that have oc-

curred during the event (see Fig. 5), whereas the synthetic

100-year event simulation neglects these breaches but in-

cludes a levee breach scenario at the March tributary Zaya

(Humer and Schwingshandl, 2009b). This naturally results

in significant differences in the inundation areas as well as

the hydraulic impact. Hence, there is greater exposure of the

Northern Railway to the real event in 2006 and the respective

total losses are more than 1.6 times higher than for the syn-

thetic 100-year event (see Table 3a and b). The results clearly

indicate the strong sensitivity of the flood damage model on

the hydraulic input and its underlying assumptions.

Furthermore, it should be noted that the March flood af-

fected only slightly more than 10 km of the Northern Rail-



Table 3. Estimated frequencies of damage classes and resulting repair costs for (a) the March flood in 2006 and (b) for different hydraulic

scenarios.

Damage class 1 Damage class 2 Damage class 3∑

(a)

n 30 54 39 123

Repair costs EUR 351 000 EUR 7 319 700 EUR 27 385 800 EUR 35 056 500

(b)

HQ30n 10 52 15 77


HQ100n 21 74 16 111


HQ300n 9 96 114 219


way track, whereas the flood damage model states 12.3 km

of exposure based on the hydraulic input. This discrepancy

can have numerous reasons such as insufficiently detailed in-

formation on local flood characteristics or mobile/temporal

flood protection measures not being considered in the setup

of the hydraulic simulation. Regarding the latter point, mas-

sive efforts were made during the event by the local fire

brigade, the Austrian Armed Forces, emergency services

and the police (Bezirksfeuerwehrkommando Gänserndorf,

2006). In the aftermath of the March flood event, existing

technical flood protection measures have been refurbished,

extended and upgraded with state-of-the-art technology in or-

der to achieve an appropriate level of protection (HQ100) for

flood-prone areas at the March River.

4.2 Flood scenarios

In a subsequent step, the damage model was applied to a set

of hydraulic scenarios complying with synthetic 30-, 100-

and 300-year March River floods. The selected return peri-

ods play a major role in various natural hazard management

strategies in Austria. For instance, the same return periods

serve as a basis in the preparation of hazard zone maps by

the Austrian Avalanche and Torrent Control (WLV). Figure 6

depicts the model results for the different synthetic scenarios

sorted in ascending order according to maximum water lev-

els. The maps show the individual inundation areas includ-

ing water levels as well as the classified damage at flood-

affected track segments. Primarily induced by an increasing

size of the inundation area as well as higher water levels, the

Northern Railway is increasingly exposed with decreasing

probability of flooding. As a consequence thereof, the num-

ber of affected track segments as well as the related damage

potential is rising. The model results for the estimation of

monetary losses are shown in Table 3b. Basically, the calcu-

lated costs amount to a plausible order and scale as the to-

tal costs increase for lower probability events. Although the

uncertainties of estimations are not being quantified, the in-

formation on the order of loss magnitudes alone is already

valuable for risk management.

Within the scope of risk assessments, the expected annual

damage (EAD) is also a common risk metric. The EAD is

defined as the annual monetary loss that is to be statistically

expected on the basis of selected hazard scenarios. Consider-

ing the available scenario bandwidth (HQ30–HQ300) in this

case study, the EAD amounts to EUR 839 721. Herein, the

share of loss equals to 46 % for the low-probability events

(HQ100–300) and 54 % for the high-/medium-probability

events (HQ30–HQ100).

4.3 Results of the model comparison

In the final part of the study, the RAIL model was compared

with the depth-damage-curve-based approaches of both the

RAM and the DSM. Table 4a (March flood) and b (synthetic

scenarios) show the results of loss estimation with RAM and

DSM as well as the corresponding difference factors to the

results of the RAIL model. As already mentioned in the intro-

duction paragraph, the RAM and the DSM tend to underesti-

mate damage to infrastructure for various reasons. The differ-

ence factors to the RAIL model fortify this finding, at least

for railway infrastructure: the RAM estimations amount to

only around a fourth of the losses compared to the results of

the RAIL model. Although the DSM results are significantly

better in line with our calculations, there is still a notable

underestimation of around 10 to 30 % of total losses except

for the HQ100 scenario, where the costs are overestimated

by around 10 %. Moreover, the absolute difference becomes

stronger with rising event return period. Both comparative

models seem to have no particular bias to high (or low) wa-

ter levels, since there is no consistent increase (or decrease)

in the difference factor with changing event probability and,

associated therewith, alternating water level magnitudes.



Figure 6. Estimation of damage potentials at the Northern Railway for three flood scenarios. The left map shows the model results for the

hydraulic input of a synthetic 30-year event. The results for a synthetic 100-year event are illustrated in the middle map. The right map covers

the results of the model application with the hydraulic input of a 300-year design event. In contrast to the hydraulic input of the March flood

in 2006, the three levee breaches were not considered in these design events. Instead, a levee breach scenario at the March tributary Zaya

was included (see pink dot). Hence, although the March River flood in 2006 was classified as a 100-year event, significant differences to the

synthetic 100-year event can be identified (e.g. inundation area, local water levels).

Table 4. (a) Calculated monetary losses for the March flood in 2006

according to the Rhine-Atlas Model (RAM) and the Damage Scan-

ner Model (DSM). (b) Calculated monetary losses for the synthetic

flood scenarios according to RAM and DSM.

RAM Difference DSM Difference

factor factor

to RAIL to RAIL

(a)

EUR 8 099 812 4.3 EUR 29 162 547 1.2

(b)

HQ30 EUR 3 809 787 4.6 EUR 15 219 675 1.2

HQ100 EUR 5 643 006 3.8 EUR 23 178 842 0.9

HQ300 EUR 22 688 580 4.1 EUR 73 126 300 1.3

Indeed, the evaluation of the RAM and DSM via the dif-

ference factor is relativised by the fact that our developed ap-

proach of damage modelling to infrastructure could not have

been validated yet due to lack of data. Nevertheless, the com-

parison of the RAM and DSM results for flooding in 2006

with the official repair costs of the ÖBB proves that the esti-

mations are significantly biased, especially when considering

that these reference costs refer only to the restoration of the

railway standard cross-section (approx. EUR 34.3 million)

and do not include the repair costs of other railway infras-

tructure elements, which would imply additional costs of

approximately EUR 7 million (Moran et al., 2010a; ÖBB-

Infrastruktur AG, personal communication, 2014). Hence,

the findings of this comparison indicate the relevance of the

level of detail in the input data that are used for the derivation

of damage functions as well as the variety of exposed assets

to be considered in the damage model. Since both the RAM

and the DSM use aggregated land-use data as input values,

they are based on a certain degree of generalisation. Thus, the

damage to railway infrastructure only marginally contributes

to total damage as it is only one out of many damage cate-

gories with varying asset values and spatial configurations.

Nevertheless, despite their similar modelling approach, the

DSM obtains far better loss estimates in our case study. This

can be explained by the fact that the DSM damage function

better reflects the real damage evolution with respect to rail-

way infrastructure. In contrast, the RAM curve does not suffi-

ciently differentiate between certain assets of infrastructure.

Instead, the approach is based on a rough average of direct

tangible losses over the entire land-use class including com-

paratively low assets, which adversely affects the loss esti-

mations solely for expensive infrastructure elements such as

railway system components.



5 Conclusions

The purpose of the approach presented in this paper was to

initially estimate the expected structural damage for a given

flood impact at exposed track sections. This step frequently is

skipped in existing flood damage models as only (relative or

absolute) monetary losses are computed. However, the local-

isation of significant structural damage potentials at specific

track section and, coupled therewith, the identification of

risk hot spots creates great added value for railway construc-

tors and operators in terms of network and risk management.

Such information allows, for example, the targeted planning

and implementation of (technical) risk reduction measures.

In this regard, the model performance already proves expedi-

ent as the mapped results plausibly illustrate the high damage

potential of the track section located closely adjacent to the

course of the river March (see Figs. 5 and 6) as well as a

general accordance with inundation depths.

Basically, the RAIL model can be applied not only to esti-

mate flood damage and related costs for specific railway lines

but also to an entire railway network, providing the following

two conditions are met: first, the general construction char-

acteristics of the infrastructure must be similar to the ones

of the Austrian Northern Railway. Accordingly, slab tracks

(i.e. high-speed railway lines), for example, are not suitable

to be investigated by RAIL since their construction design is

significantly different from the design of the Northern Rail-

way line and, hence, the derived correlations of flood im-

pact and resulting damage are no longer valid. Second, since

the RAIL model was derived from flood impacts caused by

rather low flow velocities, i.e. static river flooding, and has

not yet been tested for other flood types such as flash floods,

it is assumed that the RAIL mode is in a first instance valid

for lowland rivers. This aspect needs to be considered for

an application to a broader railway network being at risk of

flooding, particularly in countries with complex topography.

In Austria, for example, around 65 % of the national terri-

tory is located in Alpine areas mainly characterized by high

relief energy and steep slopes. In such topography, fluvial

natural events often show hydraulic characteristics being sig-

nificantly different to static river flooding, e.g. regarding the

flow velocity. Further cases and data are needed to adapt the

RAIL model to such conditions.

The RAIL model could not yet be validated by an inde-

pendent data set. Respective reviews are thus required when

appropriate empirical data are available, and further research

on potential sources of uncertainty is needed (see Sect. 3).

On the latter point we intend to put special emphasis on the

flow velocity v as this parameter is considered to also have

substantial impact on railway infrastructure above a certain

magnitude. Its investigation was not suitable so far due to

the fact that the March flood in 2006 – being classified as a

static river flood – was characterised by very low flow veloc-

ities. Therefore, testing the model’s performance in estimat-

ing structural damage caused by a dynamic flood event with

high flow velocities is strived for.

Further reviewing the model’s loss estimation is another

issue of concern. Although the approach was calibrated to

real expenses due to flooding in 2006, a verification of the

loss estimation accuracy against independent loss events is

still missing due to data scarcity. Nevertheless, its compari-

son to the RAM and DSM loss estimations for the available

scenarios points out that our presented approach is well under

way. The most obvious difference between the RAIL model

and the established tools lies in the model characteristics it-

self. While our approach is developed and specified only for

railway infrastructure, the other two models focus on flexi-

bility in application in a generalized manner, which of course

affects their model accuracy for selective applications.

Overall, the findings of this study show that the develop-

ment of reliable flood damage models is heavily constrained

by the continuing lack of detailed event and damage data. Fu-

ture research in natural risk should focus on the development

of event and damage documentation procedures to overcome

this significant hurdle in flood damage modelling.

Acknowledgements. The authors gratefully acknowledge the

Austrian Federal Railways ÖBB for their substantial data supply

and Raimund Heidrich from the engineering office riocom for his

collaboration, data supply and advice concerning the hydraulic

simulations of the March River. The research leading to these

results has received funding from the EU Seventh Framework

Programme, through the project ENHANCE (Enhancing risk

management partnerships for catastrophic natural hazards in

Europe) under grant agreement no. 308438.

Edited by: L. Ferraris

Reviewed by: J. Mysiak and another anonymous referee

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